16,917 research outputs found
A Dialogue of Multipoles: Matched Asymptotic Expansion for Caged Black Holes
No analytic solution is known to date for a black hole in a compact
dimension. We develop an analytic perturbation theory where the small parameter
is the size of the black hole relative to the size of the compact dimension. We
set up a general procedure for an arbitrary order in the perturbation series
based on an asymptotic matched expansion between two coordinate patches: the
near horizon zone and the asymptotic zone. The procedure is ordinary
perturbation expansion in each zone, where additionally some boundary data
comes from the other zone, and so the procedure alternates between the zones.
It can be viewed as a dialogue of multipoles where the black hole changes its
shape (mass multipoles) in response to the field (multipoles) created by its
periodic "mirrors", and that in turn changes its field and so on. We present
the leading correction to the full metric including the first correction to the
area-temperature relation, the leading term for black hole eccentricity and the
"Archimedes effect". The next order corrections will appear in a sequel. On the
way we determine independently the static perturbations of the Schwarzschild
black hole in dimension d>=5, where the system of equations can be reduced to
"a master equation" - a single ordinary differential equation. The solutions
are hypergeometric functions which in some cases reduce to polynomials.Comment: 47 pages, 12 figures, minor corrections described at the end of the
introductio
Beyond Inflation: A Cyclic Universe Scenario
Inflation has been the leading early universe scenario for two decades, and
has become an accepted element of the successful `cosmic concordance' model.
However, there are many puzzling features of the resulting theory. It requires
both high energy and low energy inflation, with energy densities differing by a
hundred orders of magnitude. The questions of why the universe started out
undergoing high energy inflation, and why it will end up in low energy
inflation, are unanswered. Rather than resort to anthropic arguments, we have
developed an alternative cosmology, the Cyclic universe, in which the universe
exists in a very long-lived attractor state determined by the laws of physics.
The model shares inflation's phenomenological successes without requiring an
epoch of high energy inflation. Instead, the universe is made homogeneous and
flat, and scale-invariant adiabatic perturbations are generated during an epoch
of low energy acceleration like that seen today, but preceding the last big
bang. Unlike inflation, the model requires low energy acceleration in order for
a periodic attractor state to exist. The key challenge facing the scenario is
that of passing through the cosmic singularity at t=0. Substantial progress has
been made at the level of linearised gravity, which is reviewed here. The
challenge of extending this to nonlinear gravity and string theory remains.Comment: 27 pages, 6 figures, talk given at the Nobel Symposium `String Theory
and Cosmology', 2003. To appear, Physica Script
Density Perturbations in the Ekpyrotic Scenario
We study the generation of density perturbations in the ekpyrotic scenario
for the early universe, including gravitational backreaction. We expose
interesting subtleties that apply to both inflationary and ekpyrotic models.
Our analysis includes a detailed proposal of how the perturbations generated in
a contracting phase may be matched across a `bounce' to those in an expanding
hot big bang phase. For the physical conditions relevant to the ekpyrotic
scenario, we re-obtain our earlier result of a nearly scale-invariant spectrum
of energy density perturbations. We find that the perturbation amplitude is
typically small, as desired to match observation.Comment: 36 pages, compressed and RevTex file, one postscript figure file.
Minor typographical and numerical errors corrected, discussion added. This
version to appear in Physical Review
Asymptotic safety in the f(R) approximation
In the asymptotic safety programme for quantum gravity, it is important to go
beyond polynomial truncations. Three such approximations have been derived
where the restriction is only to a general function f(R) of the curvature R>0.
We confront these with the requirement that a fixed point solution be smooth
and exist for all non-negative R. Singularities induced by cutoff choices force
the earlier versions to have no such solutions. However, we show that the most
recent version has a number of lines of fixed points, each supporting a
continuous spectrum of eigen-perturbations. We uncover and analyse the first
five such lines. Sensible fixed point behaviour may be achieved if one
consistently incorporates geometry/topology change. As an exploratory example,
we analyse the equations analytically continued to R<0, however we now find
only partial solutions.We show how these results are always consistent with,
and to some extent can be predicted from, a straightforward analysis of the
constraints inherent in the equations.Comment: Latex, 66 pages, published version, typos correcte
Modulated Perturbations from Instant Preheating after new Ekpyrosis
We present a mechanism to transfer the spectrum of perturbations in a scalar
isocurvature field onto the matter content in the radiation era via
modulated, instant preheating after ekpyrosis. In this setup, determines
the coupling constant relevant for the decay of a preheat matter field into
Fermions. The resulting power spectrum is scale invariant if remains
close to a scaling solution in new ekpyrotic models of the universe; by
construction the spectrum is independent of the detailed physics near the
bounce. The process differs from the curvaton mechanism, which has been used
recently to revive the ekpyrotic scenario, in that no peculiar behavior of
shortly before or during the bounce is needed. In addition, a concrete
and efficient realization of reheating after ekpyrosis is provided; this
mechanism is not tied to ekpyrotic models, but could equally well be used in
other setups, for instance inflationary ones. We estimate non-Gaussianities and
find no additional contributions in the most simple realizations, in contrast
to models using the curvaton mechanism.Comment: 21 pages; v2 references added, minor clarification
Passing through the bounce in the ekpyrotic models
By considering a simplified but exact model for realizing the ekpyrotic
scenario, we clarify various assumptions that have been used in the literature.
In particular, we discuss the new ekpyrotic prescription for passing the
perturbations through the singularity which we show to provide a spectrum
depending on a non physical normalization function. We also show that this
prescription does not reproduce the exact result for a sharp transition. Then,
more generally, we demonstrate that, in the only case where a bounce can be
obtained in Einstein General Relativity without facing singularities and/or
violation of the standard energy conditions, the bounce cannot be made
arbitrarily short. This contrasts with the standard (inflationary) situation
where the transition between two eras with different values of the equation of
state can be considered as instantaneous. We then argue that the usually
conserved quantities are not constant on a typical bounce time scale. Finally,
we also examine the case of a test scalar field (or gravitational waves) where
similar results are obtained. We conclude that the full dynamical equations of
the underlying theory should be solved in a non singular case before any
conclusion can be drawn.Comment: 17 pages, ReVTeX 4, 13 figures, minor corrections, conclusions
unchange
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